Elliptic curve isogeny class 22400.7-i over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-22400.7-i
• Conductor: 22400.7
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 22400.7-i over \(\Q(\sqrt{-7}) \)

Isogeny class 22400.7-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
22400.7-i1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a\) , \( -3 a + 28\bigr] \)
22400.7-i2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 14 a - 30\) , \( -48 a + 44\bigr] \)
22400.7-i3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 26 a - 18\) , \( 42 a + 12\bigr] \)
22400.7-i4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -103 a + 100\) , \( -123 a + 668\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph